# Law of Variable Proportion: Detailed Explanation

Imagine, you are standing at your favourite ice cream parlour and eagerly waiting to gobble it up, and you start eating the scoops one after the other continuously. At first, your satisfaction level is at its highest peak and After having 3 or 4 scoops, your level is still increasing, but now at a diminishing rate. Eventually, a point will come when you will be almost close to being satisfied and full, there would be lesser chances for you to eat another scoop. This is exactly what the Law of Variable Proportion means. Being one of the most popular concepts in the field of Business Economics and Managerial Economics, here is an insightful blog to help you understand every aspect of the law.

Must Read: Types of Economy Explained

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## What is the Law of Variable Proportions?

The Law of Variable Proportions states that as the quantity of a factor is increased while keeping other factors constant, the Total Product (TP) first rises at an incremental rate, then at a decremental rate and lastly the total production begins to fall. In other words, as one of the factors in production makes some variation in its quantity, keeping all the other factors constant, the ratio between all the factors starts varying, which further influence the level of output.

## Assumptions

The law of variable proportion works under the following situations:

• Constant State of Technology
The first assumption is that the state of technology given for the situation remains unchanged. In case, the technology gets improved, then the marginal product may rise rather than diminish.
• Other Factors also remain fixed
This means that there should some inputs or factors given in a certain situation which should remain fixed in terms of their quantity. By changing the factor proportions, we can understand the effects on the output. However, the law would not work if all the factors are altered in proportions.
• Possibility of Varying the Proportions of Factors
The third assumption is that the law can only work if there is the scope for varying proportions of factors as fixed proportions might not yield effective results.

## Terms to Remember

Before we go ahead with a detailed explanation of the law, let us first understand the different terms that we will be using in this blog:

## What are the Stages of Law of Variable Proportion?

In order to understand this in detail, let us take an example. Imagine you own a land wherein you produce rice by employing more and more labour (variable factors). The table given below explains the situation further: 3 Stages of Law of Variable Proportion

In the above table and graph of the Law of Variable Proportions, you would notice that:

• Up to 3 units of labour employed, the TP is rising at an increasing rate (2,6,12). This constitutes Stage 1 of the law, which is the Stage of Increasing Returns. Therefore, during the first stage, the TP curve increases significantly.
• Beyond the 3rd unit of labour, the TP starts rising at a diminishing rate (12,16,18), which means the TP curve rises at a slower rate. This eventually makes the marginal product (MP) starting to fall. Constituting the second stage of the Law of Variable Proportion which is called the Stage of Diminishing Returns.
• After the employment of 6 units of labour, the TP starts to fall, indicating the 3rd stage which is the Stage of Negative Returns. Even after employing 6 units of labour, it fails to yield the marginal product, that is when the MP comes to zero. Eventually, the TP curve starts sloping down and the marginal product goes to negative in the x-axis.

## Relation Between TP, MP and AP

Now that we know how all the 3 aspects behave in all the three stages of the Law of Variable Proportion, let us provide you with an insight on how these three factors are related to each other.

1. When TP increases at an increasing rate, the MP and AP also increase. However, at this stage, MP>AP
2. When TP increases at a decreasing rate, the MP and AP start to fall. When MP starts falling significantly and AP falls at a low rate, it means that now MP<AP.
3. When TP falls, MP goes negative and AP falls consistently remaining above the x-axis.
4. MP intersects AP when the latter is at the maximum, this is where MP=AP.

Now arises a Million Dollar Question. Which stage of the Law of Variable Proportion should a firm operate in? Is it Stage 1, 2 or 3? Let’s have you a simple answer to this question.

As a rational firm, the optimal utilization of both the fixed and variable inputs would take place only in Stage 2 of the Law of Variable Proportion. That is the only time when all the inputs are used in an economical way. Additionally, the MP and AP of both the inputs are positive yet diminishing. Whereas, is a firm operates in the first stage, the marginal product of the fixed input (land) is still in a negative form. This is because the lesser units of labour are using the land in large proportion, thereby yielding no marginal product.

You must be surprised to know that the Law of Variable Proportion has universal applicability in any branch of production. Forming the basis of a number of doctrines in Economics, students can understand its role in the study of the Theory of Production. So if you’re looking forward to building a career in Economics and need assistance in choosing the right university abroad, talk to us at Leverage Edu.

1. Mohit Lahri says:

thanks a lot, your explanation is very easy

1. Team Leverage Edu says:

Hey Mohit, we are glad that you found the blog easy to understand.

2. Matthew says:

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1. Team Leverage Edu says:

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